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Let G="(V,E) be a simple graph, and for all v∈V, let L v) be a list of colors assigned to v. We shall assume throughout that the colors are natural numbers.
Let G="(V,E) be a simple graph with vertex set V and edge set E. A subset W⊆V∪E is a mixed dominating set if every element x∈(V∪E)∖W is either adjacent or incident to an element of W. The mixed domination problem is to find a minimum mixed dominating set of G.
Let be a simple graph with vertices.
Let G be a simple graph.
Let G be a simple graph with n vertices.
Let (G= V, E)) be a simple graph.
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A nonincreasing sequence d="(d1,d2,…,dn) is graphic if there is a simple graph G with degree sequence d.
An ˜RMP k,λ n,m) (resp. ˜RMC k,λ n,m)) is a resolvable packing (resp. covering) with maximum (resp. minimum) possible number m of parallel classes which are mutually distinct, each parallel class consists of ⌊(n−k+1)/k⌋ blocks of size k and one block of size n−k⌊(n−k+1)/k⌋, and its leave (resp. excess) is a simple graph.
Definition 1: G V, E) is a simple graph with m vertices and n edges.
The circulant graph can be defined as follows [2, 13]: Definition 1: G V, E) is a simple graph with m vertices and n edges.
First, a so-called molecular supergraph is constructed which is a simple graph such that the molecular graphs of all training set structures can be represented as its subgraphs.
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